Testing the equality of proportions for correlated otolaryngologic data

In otolaryngologic (or ophthalmologic) studies, each subject usually contributes information for each of two ears (or eyes), and the values from the two ears (or eyes) are generally highly correlated. Statistical procedures that fail to take into account the correlation between responses from two ears could lead to incorrect results. On the other hand, asymptotic procedures that overlook small sample designs, sparse data structures, or the discrete nature of data could yield unacceptably high type I error rates even when the intraclass correlation is taken into consideration. In this article, we investigate eight procedures for testing the equality of proportions in such correlated data. These test procedures will be implemented via the asymptotic and approximate unconditional methods. Our empirical results show that tests based on the approximate unconditional method usually produce empirical type I error rates closer to the pre-chosen nominal level than their asymptotic tests. Amongst these, the approximate unconditional score test performs satisfactorily in general situations and is hence recommended. A data set from an otolaryngologic study is used to illustrate our proposed methods.